Discrete droplet microfluidic systems—where droplets move through a bulk fluid in interconnected network of channels—are a rapidly expanding technology with exciting applications that cross-cut several scientific and engineering endeavors [14,31-39]. Millions of very small volume droplets in the nanoliter range can be reproducibly generated and processed in these droplet-based microfluidic systems. This allows for unparalleled control over small volumes of materials in time and space, which has revolutionized conventional biochemical analysis [1,2]. Recent advances in this area have led to the development of devices with basic functionalities such as sorting [3,4,5], merging [6], synchronization[7] and storing [8,9,10]. Using these basic devices it is now possible to design massively parallelized large-scale architectures for lab-on-chip applications. The current state-of-the-art is that these devices are developed using a bottom up approach i.e. by rigorous experimentation to find optimal designs for a given objective.
One important consequence of this control is the ability to investigate the physics and chemistry of materials at a single entity level. This can lead to transformative science where, for example, each cell from a large population of cells could be analyzed for cancer and other possible diseases [40-42]. This also makes high-throughput chemistry possible since one could conceivably ensure that every molecule undergoes the same “processing experience”. Microfluidic sensors with detection specificity in the parts per billion scales [43-45] can be imagined.
While the promise of this field of science is enormous, ultimate realization of this potential depends on engineering devices that have precise and multiple functionalities while being robust to the inevitable design and environmental uncertainties. While individual processor designs are being generated at a frenetic pace, identifying designs that efficiently integrate these processors in large-scale droplet-based microfluidic platforms is still very much an emerging science. Consider a case where one wants to know if there exists, for a particular application, a large-scale droplet-based microfluidic platform that offers multiple desired functions with a small footprint? While this in itself is a difficult question to answer routinely, a more involved question is, even if such a design exists, how much of this multi-functionality is retained in the face of inevitable experimental uncertainties? While it might certainly be possible to formulate answers to such questions with minimal experimentation in fields where decades of prior design knowledge exists, this is rather unlikely in newer areas such as droplet-based microfluidics.
Designing these devices in order to achieve specific functionality, such as spatial and temporal control of the droplets, is a laborious process that involves several experimental trials. Microfluidic ladder network is one such device that has shown to passively control droplet spacing. It is important to optimize design parameters such as number of bypasses, their orientation and spacing between them to realize all the functionalities offered by these devices.
Several papers have studied the ladder network in detail. The ladder networks are important in their own right and have been used in microfluidic networks for synchronization. Synchronizer is an operation used to maintain a zero or relatively small time difference between two events such as droplets exiting two arms of a ladder. Droplets entering the two arms of the ladder at different times but synchronized by the time they leave the ladder. The bypasses (i.e. steps of the ladder) allow the bulk fluid to flow through but forbid the passage of droplets. While the underlying physical principle of the synchronizer is deceptively simple, yet trying to design a robust synchronizer with minimal device foot-print under unavoidable experimental constraints is not trivial. For example in the pursuit of a robust synchronizer, one might ask what is the optimal number of bypasses needed and how does this number depend on droplet hydrodynamic resistance and velocities. What degree of experimental uncertainties can be tolerated and yet achieve acceptable synchronizer functionality? Are there alternative and more efficient structural configurations for the synchronizer than that implemented by Prakash and Gershenfeld [37]? Is it possible to design a ladder network for multiple functionalities such as input delay dependent behavior? Are there any advantages that can be accrued by slanting the arms of the ladder either in the forward or backward directions? To answer these questions, currently neither systematic efforts have been devoted nor rational approaches have been developed.